@article{Yu2024, 
author = {Lujuan Yu and Beibei Wang and Jianwei Yang},
title = {An eigenvalue problem related to the variable exponent double-phase operator},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {1664-1682},
keywords = {double-phase problem, eigenvalues, ∞-Laplacian, viscosity solution, variable exponents},
url = {https://www.sciopen.com/article/10.3934/math.2024082},
doi = {10.3934/math.2024082},
abstract = {In this paper, we studied a double-phase eigenvalue problem with large variable exponents. Let        λ          (              p                  n                    (      ⋅      )      ,                    q                  n                    (      ⋅      )      )              1       be the first eigenvalues and        u          n       be the first eigenfunctions, normalized by    ‖      u          n            ‖                            H                          n                      =  1. Under some assumptions on the variable exponents        p          n        (  ⋅  ) and        q          n        (  ⋅  ), we showed that        λ          (              p                  n                    (      ⋅      )      ,                    q                  n                    (      ⋅      )      )              1       converges to        Λ          ∞      ,        u          n       converges to        u          ∞       uniformly in the space        C          α        (  Ω  )    (  0  <  α  <  1  ) and        u          ∞       is a nontrivial viscosity solution to a Dirichlet    ∞-Laplacian problem. Even in the case where the variable exponents reduce to the constant exponents, our work is the first one dealing with a double-phase eigenvalue problem with large exponents.}
}